HSC Extension 1 and 2 Mathematics/3-Unit/Preliminary/Harder 2-Unit

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Implicit differentiation[edit]

Implicit differentiation is a method of differentiating an expression in and , where and are related in some manner and neither are constant.

For example, one could differentiate with respect to as follows:

Using the chain rule:

It is useful to think of implicit differentiation as normal differentiation with respect to , only whenever you come across a term with , you multiply the differentiated term by .

Another example: find the derivative of

Working: